{"id":"https://openalex.org/W4392004136","doi":"https://doi.org/10.22331/q-2024-02-21-1261","title":"Stabilizer Formalism for Operator Algebra Quantum Error Correction","display_name":"Stabilizer Formalism for Operator Algebra Quantum Error Correction","publication_year":2024,"publication_date":"2024-02-21","ids":{"openalex":"https://openalex.org/W4392004136","doi":"https://doi.org/10.22331/q-2024-02-21-1261"},"language":"en","primary_location":{"id":"doi:10.22331/q-2024-02-21-1261","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-02-21-1261","pdf_url":"https://quantum-journal.org/papers/q-2024-02-21-1261/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2024-02-21-1261/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034041742","display_name":"Guillaume Dauphinais","orcid":null},"institutions":[{"id":"https://openalex.org/I4210150097","display_name":"Xanadu Quantum Technologies (Canada)","ror":"https://ror.org/05qj0n416","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210150097"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Guillaume Dauphinais","raw_affiliation_strings":["Xanadu, Toronto, ON M5G 2C8, Canada"],"affiliations":[{"raw_affiliation_string":"Xanadu, Toronto, ON M5G 2C8, Canada","institution_ids":["https://openalex.org/I4210150097"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010856269","display_name":"David W. Kribs","orcid":"https://orcid.org/0000-0001-9010-1144"},"institutions":[{"id":"https://openalex.org/I79817857","display_name":"University of Guelph","ror":"https://ror.org/01r7awg59","country_code":"CA","type":"education","lineage":["https://openalex.org/I79817857"]},{"id":"https://openalex.org/I4210150097","display_name":"Xanadu Quantum Technologies (Canada)","ror":"https://ror.org/05qj0n416","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210150097"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David W. Kribs","raw_affiliation_strings":["Department of Mathematics & Statistics, University of Guelph, Guelph, ON N1G 2W1, Canada","Xanadu, Toronto, ON M5G 2C8, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, University of Guelph, Guelph, ON N1G 2W1, Canada","institution_ids":["https://openalex.org/I79817857"]},{"raw_affiliation_string":"Xanadu, Toronto, ON M5G 2C8, Canada","institution_ids":["https://openalex.org/I4210150097"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039026944","display_name":"Michael Vasmer","orcid":"https://orcid.org/0000-0002-6711-5924"},"institutions":[{"id":"https://openalex.org/I4210150097","display_name":"Xanadu Quantum Technologies (Canada)","ror":"https://ror.org/05qj0n416","country_code":"CA","type":"company","lineage":["https://openalex.org/I4210150097"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michael Vasmer","raw_affiliation_strings":["Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada","Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada","Xanadu, Toronto, ON M5G 2C8, Canada"],"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada","institution_ids":["https://openalex.org/I183974707"]},{"raw_affiliation_string":"Xanadu, Toronto, ON M5G 2C8, Canada","institution_ids":["https://openalex.org/I4210150097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5034041742"],"corresponding_institution_ids":["https://openalex.org/I4210150097"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.8013,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.86195648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"8","issue":null,"first_page":"1261","last_page":"1261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.6561975479125977},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6383706331253052},{"id":"https://openalex.org/keywords/stabilizer","display_name":"Stabilizer (aeronautics)","score":0.553377091884613},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5023658275604248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4921724200248718},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4421502351760864},{"id":"https://openalex.org/keywords/operator-algebra","display_name":"Operator algebra","score":0.44096243381500244},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41218122839927673},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3248184621334076},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3017919063568115},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.25677594542503357},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.16606155037879944},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09325993061065674},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.057170480489730835}],"concepts":[{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6561975479125977},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6383706331253052},{"id":"https://openalex.org/C2777502316","wikidata":"https://www.wikidata.org/wiki/Q2712515","display_name":"Stabilizer (aeronautics)","level":2,"score":0.553377091884613},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5023658275604248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4921724200248718},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4421502351760864},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.44096243381500244},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41218122839927673},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3248184621334076},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3017919063568115},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.25677594542503357},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.16606155037879944},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09325993061065674},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.057170480489730835},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2024-02-21-1261","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-02-21-1261","pdf_url":"https://quantum-journal.org/papers/q-2024-02-21-1261/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:53dcb5210c9c42238e1eea03e32d8ad8","is_oa":true,"landing_page_url":"https://doaj.org/article/53dcb5210c9c42238e1eea03e32d8ad8","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 8, p 1261 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2024-02-21-1261","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-02-21-1261","pdf_url":"https://quantum-journal.org/papers/q-2024-02-21-1261/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2591634599","display_name":null,"funder_award_id":"400160","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320312716","display_name":"Innovation, Science and Economic Development Canada","ror":"https://ror.org/03zp01h17"},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"},{"id":"https://openalex.org/F4320331473","display_name":"Ministry of Colleges and Universities","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392004136.pdf"},"referenced_works_count":80,"referenced_works":["https://openalex.org/W142413548","https://openalex.org/W1546322230","https://openalex.org/W1602420091","https://openalex.org/W1934222401","https://openalex.org/W1982432882","https://openalex.org/W1984125696","https://openalex.org/W1987890035","https://openalex.org/W1999706070","https://openalex.org/W1999770545","https://openalex.org/W2002324453","https://openalex.org/W2005225046","https://openalex.org/W2006275843","https://openalex.org/W2039302501","https://openalex.org/W2069711632","https://openalex.org/W2081230419","https://openalex.org/W2083041493","https://openalex.org/W2091331782","https://openalex.org/W2095025840","https://openalex.org/W2098838878","https://openalex.org/W2110207229","https://openalex.org/W2114207424","https://openalex.org/W2116102644","https://openalex.org/W2127688694","https://openalex.org/W2131690084","https://openalex.org/W2132886647","https://openalex.org/W2135273380","https://openalex.org/W2153598200","https://openalex.org/W2167927798","https://openalex.org/W2224517465","https://openalex.org/W2301659878","https://openalex.org/W2301999234","https://openalex.org/W2485945841","https://openalex.org/W2581931326","https://openalex.org/W2594901681","https://openalex.org/W2763302490","https://openalex.org/W2781738013","https://openalex.org/W2883347043","https://openalex.org/W2895656445","https://openalex.org/W2901960432","https://openalex.org/W2945121003","https://openalex.org/W2951987143","https://openalex.org/W2952602009","https://openalex.org/W2963033819","https://openalex.org/W2963734035","https://openalex.org/W2963760674","https://openalex.org/W2982554234","https://openalex.org/W2990961515","https://openalex.org/W3013492608","https://openalex.org/W3014422752","https://openalex.org/W3088076771","https://openalex.org/W3092581746","https://openalex.org/W3092764718","https://openalex.org/W3098035205","https://openalex.org/W3100931082","https://openalex.org/W3101551690","https://openalex.org/W3102142151","https://openalex.org/W3102352811","https://openalex.org/W3104330661","https://openalex.org/W3105525551","https://openalex.org/W3106082980","https://openalex.org/W3106164661","https://openalex.org/W3106438908","https://openalex.org/W3111565275","https://openalex.org/W3119777061","https://openalex.org/W3126262297","https://openalex.org/W3174724359","https://openalex.org/W3175087006","https://openalex.org/W3181439919","https://openalex.org/W3195308044","https://openalex.org/W3202447927","https://openalex.org/W3213933684","https://openalex.org/W3213943817","https://openalex.org/W3216176305","https://openalex.org/W4281479206","https://openalex.org/W4285597627","https://openalex.org/W4288090586","https://openalex.org/W4307203248","https://openalex.org/W4321610982","https://openalex.org/W4385625257","https://openalex.org/W4394672652"],"related_works":["https://openalex.org/W2392919231","https://openalex.org/W2373888082","https://openalex.org/W2384382117","https://openalex.org/W4252630758","https://openalex.org/W2043828253","https://openalex.org/W2368845495","https://openalex.org/W2352943411","https://openalex.org/W2369119520","https://openalex.org/W2566068142","https://openalex.org/W2358365047"],"abstract_inverted_index":{"We":[0,77,106],"introduce":[1],"a":[2,51,63,97],"stabilizer":[3,46,75],"formalism":[4],"for":[5,23,32,62,70],"the":[6,56,67,71,82,88,93,101,118],"general":[7],"quantum":[8,15,25,34],"error":[9,16,26,35],"correction":[10,17,36],"framework":[11],"called":[12],"operator":[13,33],"algebra":[14],"(OAQEC),":[18],"which":[19],"generalizes":[20],"Gottesman&amp;apos;s":[21],"formulation":[22],"traditional":[24],"correcting":[27],"codes":[28,39,47,85],"(QEC)":[29],"and":[30,37,48,73,90,120],"Poulin&amp;apos;s":[31],"subsystem":[38,84],"(OQEC).":[40],"The":[41],"construction":[42],"generates":[43],"hybrid":[44,79,111],"classical-quantum":[45],"we":[49,91,121],"formulate":[50],"theorem":[52,94],"that":[53,59,99],"fully":[54],"characterizes":[55],"Pauli":[57],"errors":[58],"are":[60,115],"correctable":[61],"given":[64],"code,":[65],"generalizing":[66],"fundamental":[68],"theorems":[69],"QEC":[72],"OQEC":[74],"formalisms.":[76],"discover":[78],"versions":[80],"of":[81,103],"Bacon-Shor":[83],"motivated":[86],"by":[87,117],"formalism,":[89,119],"apply":[92],"to":[95,127],"derive":[96],"result":[98],"gives":[100],"distance":[102],"such":[104],"codes.":[105],"show":[107],"how":[108,124],"some":[109],"recent":[110],"subspace":[112],"code":[113],"constructions":[114],"captured":[116],"also":[122],"indicate":[123],"it":[125],"extends":[126],"qudits.":[128]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}
